Robot milling system tail end nonlinear frequency response modeling method and device and application

Abstract

The invention belongs to the technical field related to robot machining dynamics, and discloses a robot milling system tail end nonlinear frequency response modeling method and device and application, and the method comprises the steps: S1, building a robot tail end nonlinear frequency response model through experimental analysis; s2, linear kinetic parameters and nonlinear kinetic parameters of the nonlinear frequency response model are identified through a harmonic detection method, and nonlinear response of the robot milling system is analyzed based on Volterra series; and S3, identifying parameters of a joint part of the main shaft and the cutter handle based on the obtained kinetic parameters, and predicting a force / displacement frequency response function of the cutter point of the robot milling system in combination with an RCSA theory so as to realize modeling of nonlinear frequency response of the cutter point of the robot milling system. The machining time cost and the economic cost are reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field related to robot machining dynamics, and more specifically, relates to a method, device and application for modeling nonlinear frequency response of a terminal end of a robot milling system. Background Art

[0002] As a complex system with multiple degrees of freedom, robots exhibit significant nonlinear dynamic characteristics during milling. This is mainly due to the coupling of nonlinear mechanisms such as the stiffness hardening / softening effects of the revolute joints, friction, clearance, and hysteresis. In existing technologies, researchers typically use linear dynamic models to predict the vibration characteristics and stability of the milling process. However, since linear models cannot fully characterize the nonlinear behavior of the robot system, large errors occur during the process parameter optimization process. Effective identification of dynamic model parameters can improve the accuracy of robot milling and the surface quality of the workpiece, and reduce the uncertainty and complexity of model predictions.

[0003] In robotic milling systems, tool replacement can significantly change the frequency response characteristics of the tool tip, affecting machining stability and accuracy. Traditional frequency response function (FRF) acquisition methods are based on fixed tool parameters, but in actual machining, factors such as tool geometry, material properties, and clamping conditions can cause the frequency response characteristics to vary with working conditions. In existing technologies, in order to obtain the dynamic characteristics under different tool parameters, a large number of repetitive experiments and numerical simulations are often required, which not only increases time and economic costs, but also significantly prolongs the machining preparation cycle. Therefore, how to efficiently predict the tool frequency response characteristics, reduce the number of experiments, and improve efficiency while considering the nonlinear characteristics of the robot has become a technical problem that needs to be solved urgently.

[0004] Existing stability prediction methods are mostly based on the linear frequency response model of the robot end, which fails to reflect the significant nonlinear frequency response characteristics of the robot body in the low-frequency range and predict the nonlinear frequency response of the tool tip of the robot milling system. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a method, device and application for modeling the nonlinear frequency response of the end of a robotic milling system, which aims to solve the problem of high time and economic costs of existing tool parameter acquisition methods.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for modeling the nonlinear frequency response of a robot milling system end-point is provided, the method comprising the following steps:

[0007] S1, establish the nonlinear frequency response model of the robot terminal through experimental analysis;

[0008] S2, identifying the linear dynamic parameters and nonlinear dynamic parameters of the nonlinear frequency response model by a harmonic detection method, and analyzing the nonlinear response of the robot milling system based on Volterra series;

[0009] S3, based on the obtained dynamic parameters, identifies the parameters of the spindle and tool holder joint, and combines the RCSA theory to predict the force / displacement frequency response function of the tool tip of the robotic milling system to achieve the modeling of the nonlinear frequency response of the tool tip of the robotic milling system.

[0010] Furthermore, the mathematical expression of the nonlinear frequency response model is:

[0011]

[0012] Where F(t) is the manipulator end-operation force vector; M, C, and K are the mass, stiffness, and damping matrices of the robot system, respectively; q(t) is the displacement of the robot end in Cartesian space; C3 and K3 correspond to the cubic nonlinear damping matrix and the cubic nonlinear stiffness matrix, respectively.

[0013] Furthermore, the dynamic parameters in the nonlinear frequency response of the robot end are identified through an identification method based on the restoring force surface method.

[0014] Furthermore, the nonlinear stiffness and damping parameters of the nonlinear frequency response model are identified by a harmonic detection method.

[0015] Furthermore, the solution equation for the linear dynamic parameters is:

[0016]

[0017] The equations for solving the parameters of the cubic stiffness term and the cubic damping term are:

[0018]

[0019] The linear stiffness coefficient and damping coefficient are:

[0020]

[0021] The cubic stiffness coefficient and cubic damping coefficient are:

[0022] H3(ω,ω,-ω)=(-ic3ω 3 -k3)H1(ω) 3 H1(-ω)

[0023] Where m, c1, and k1 are the linear mass, damping, and stiffness parameters, respectively; c3 and k3 are the cubic nonlinear damping and cubic nonlinear stiffness parameters; and ω represents the frequency.

[0024] Furthermore, the robotic milling system is divided into a robot-spindle-tool holder substructure and a tool substructure. Based on the nonlinear frequency response of the end of the robot-spindle-tool holder subsystem, the Timoshenko beam theory is used to model the dynamic characteristics of the tool substructure, and then the RCSA theory is combined to predict the force / displacement frequency response function of the tool tip point of the robotic milling system.

[0025] Furthermore, the force / displacement frequency response function of the tool tip of the robot milling system is:

[0026] G 11 =R 11 -R 13a B -1 R 3a1

[0027] Where B = R 3a3a +R 3b3b +R J , where R J represents the joint response matrix between the robot-spindle-toolholder substructure and the tool substructure. The corresponding expression is:

[0028]

[0029] Where k x and c x represents the linear spring stiffness and linear damping parameters, k θ and c θ are the torsional spring stiffness and torsional damping parameters, both of which are parameters of the joint between the shank and the tool.

[0030] The present invention also provides an application of the above-mentioned nonlinear frequency response modeling method of the terminal end of the robotic milling system in the vibration characteristics and stability prediction of the robotic milling system and the processing control of the robotic milling system.

[0031] The present invention also provides a nonlinear frequency response modeling system for the terminal end of a robotic milling system. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the nonlinear frequency response modeling method for the terminal end of the robotic milling system as described above.

[0032] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the above-mentioned method for modeling the nonlinear frequency response of the end of the robotic milling system.

[0033] In general, compared with the prior art, the above technical solutions conceived by the present invention have the following beneficial effects:

[0034] 1. This paper introduces the Volterra series to describe the nonlinear frequency response of the robot end-point. It can accurately characterize the nonlinear frequency response behavior of the robot milling system end-point caused by nonlinear joint stiffness and friction hysteresis. This solves the problem that existing robot machining vibration models generally assume that the vibration response of the tool is a linear frequency response, thereby improving accuracy. At the same time, the RCSA substructure coupling method is used to predict the tool tip frequency response function of the robot milling system. This reduces the number of frequency response test experiments, avoids a large number of repeated experiments, and reduces processing preparation time and economic costs.

[0035] 2. Based on experimental data, the particle swarm optimization algorithm is used to optimize and identify the stiffness and damping parameters of the tool holder-tool joint. This can accurately predict the tool tip frequency response function of the robotic milling system, providing a theoretical basis for drawing machining stability lobe diagrams and suppressing vibration. In actual machining applications, it can improve machining accuracy and surface quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of a nonlinear frequency response modeling method for a robot milling system terminal provided by the present invention;

[0037] Figure 2 This is a schematic diagram of the experimental platform of the robot milling system used in the present invention, showing the overall layout of the robotic arm and milling device;

[0038] Figure 3 (a), (b), (c), and (d) are the restoring force identification results of the robot milling system in step S1 of the embodiment of the present invention, and the degree of fit between the measured data and the identification results is compared;

[0039] Figure 4 (a) and (b) are respectively example diagrams of stepped sine test data used for dynamic parameter identification in step S2 of an embodiment of the present invention;

[0040] Figure 5 3 is a comparison chart of the robot terminal frequency response simulation results and the experimental test results based on the dynamic parameters identified in step S2 of the embodiment of the present invention;

[0041] Figure 6 This is a schematic diagram of the substructure division used for tool tip frequency response prediction of a robot milling system in step S3 of an embodiment of the present invention, illustrating the substructure division method and connection relationship between the robot body and the end effector;

[0042] Figure 7 (a) and (b) are respectively the nonlinear frequency responses of the tool tip of the robot milling system obtained by RCSA calculation in step S3 of the embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0044] The present invention provides a method for modeling the nonlinear frequency response of the end of a robotic milling system. The method models the nonlinear frequency response of the tool tip of the robotic milling system based on the Volterra series and the Receptance Coupling Substructure Analysis (RCSA) method. This method solves the problem that existing robotic machining vibration models generally assume that the vibration response of the tool is a linear frequency response, reduces the number of experiments for tool tip frequency response testing, and provides theoretical support for machining stability prediction and chatter suppression.

[0045] See also Figure 1 and Figure 2 , the modeling method mainly includes the following steps:

[0046] S1, establish the nonlinear frequency response model of the robot terminal through experimental analysis.

[0047] The nonlinear frequency response model systematically describes the nonlinear restoring force characteristics and frequency domain response behavior of the robot end under force, taking into account the influence of nonlinear stiffness and nonlinear damping on the frequency response characteristics; the processing robot data is obtained by performing end hammering tests and exciter tests on a six-axis industrial robot in a fixed working posture, such as Figure 2 shown.

[0048] In this embodiment, the experimental platform applies a sinusoidal excitation signal to observe the dynamic response characteristics of the robot milling system end under different excitation conditions, focusing on analyzing its nonlinear frequency response behavior near the resonant frequency. The identification method based on the restoring force surface method is used to accurately identify the type of dynamic parameters in the nonlinear frequency response of the robot end. q (t) and the measured acceleration It can be obtained from the experimental data, and the restoring force can be calculated by the following formula:

[0049]

[0050] In this process, the mass m is obtained by fitting the results of the pulse hammer test in combination with the rational polynomial method. A variable frequency sinusoidal signal near the resonant frequency is used as the excitation force to excite the resonance peak of the end frequency response of the robot milling system. At the same time, a laser displacement sensor is used to measure the vibration displacement, and the output signal of the laser vibrometer is differentiated to obtain the corresponding acceleration and velocity response. When the displacement |q(t)| is less than 0.1% of the maximum displacement, the change characteristics of the restoring force with velocity under low displacement conditions can be calculated; when the velocity When the value is less than 0.1% of the maximum speed, the variation characteristics of the restoring force with displacement under low speed conditions can be calculated.

[0051] In the restoring force model obtained through experimental identification, both the damping component and the stiffness component exhibit significant cubic nonlinear characteristics. The identification results of the restoring force are as follows: Figure 3 To express the velocity component of the restoring force, Figure 3 The red dots in (a) represent the estimated restoring force, and the blue line represents the linear restoring force estimated based on the linear damping parameters. Figure 3 (b) shows the deviation of the restoring force from the linear approximation. The blue curve in the figure represents the cubic form of the velocity. Fitted polynomial function. Similarly, in order to express the displacement component in the restoring force, Figure 3 The red dots in (c) represent the estimated restoring force, while the blue line represents the linear restoring force estimated based on the linear stiffness. Figure 3 This is more evident in (d), which depicts the deviation of the robotic milling system response from the linear stiffness estimate. The results show that the deviation from the linear stiffness also exhibits a polynomial trend, and the blue curve is the cubic polynomial form k3q(t) 3 The results of the fit are used to describe the estimation bias.

[0052] Through experimental identification of the composition of nonlinear dynamic parameters in the nonlinear frequency response of the robot terminal, both the damping component and the stiffness component exhibit significant cubic nonlinear characteristics. Based on this, the nonlinear frequency response model of the robot terminal is expressed as:

[0053]

[0054] Where F(t) is the manipulator end-operation force vector; M, C, and K are the mass, stiffness, and damping matrices of the robot system, respectively; q(t) is the displacement of the robot end in Cartesian space; C3 and K3 correspond to the cubic nonlinear damping matrix and the cubic nonlinear stiffness matrix, respectively.

[0055] The main consideration is the force generated by the milling force acting on the X and Y directions of the robot end during the machining process, that is, F(t) = [F x (t)F y (t)] T Without considering the torque generated by the milling force on the end of the robot, q(t)=[x(t)y(t)] T In the experiment, the frequency responses of the robot in each direction showed good separation, so the modal coupling effect in the X and Y directions of the robot end can be ignored. The input in a single direction of the system corresponds to the system response in that direction. The following dynamic equations can be established in the X and Y directions:

[0056]

[0057] S2, identifying the linear dynamic parameters and nonlinear dynamic parameters of the nonlinear frequency response model by a harmonic detection method, and analyzing the nonlinear response of the robot milling system based on the Volterra series.

[0058] Specifically, the nonlinear stiffness and damping parameters of the nonlinear frequency response model are identified by the harmonic detection method and verified by the Runge-Kutta method. The Runge-Kutta method is a high-precision numerical integration method for solving differential equations. In an embodiment of the present invention, it is used to calculate the time domain response of the end of the robot milling system to verify the validity of the nonlinear frequency response model of the robot end and the identified nonlinear dynamic parameters. For a nonlinear system subjected to single-frequency harmonic excitation, based on the harmonic detection method, its response can be expressed as a combination of sinusoidal motion at the excitation frequency and its harmonics. The composite frequency response function can be obtained at the excitation frequency as follows:

[0059]

[0060] The response components and harmonics of a nonlinear system under a single harmonic excitation frequency are determined by the system's composite frequency response function and the amplitude of the excitation force. Applying the Volterra harmonic detection method, the first-order FRF linear stiffness coefficient and damping coefficient are approximated as follows:

[0061]

[0062] The cubic stiffness coefficient and cubic damping coefficient can be obtained by the Volterra harmonic detection method through the approximation of the third-order FRF:

[0063] H3(ω,ω,-ω)=(-ic3ω 3 -k3)H1(ω) 3 H1(-ω)

[0064] In order to identify the linear and nonlinear parameters in the nonlinear frequency response model of the robot end, it is assumed that the single degree of freedom system consists of frequency ω and amplitude F n (n=1…N) sinusoidal force excitation, ignoring the higher-order terms above the fifth order, the frequency response Q of the system under sinusoidal force excitation with different amplitudes n (ω),n=1…N can be expressed using HFRFs and excitation amplitudes as follows:

[0065]

[0066] See also Figure 4 , after standard Fourier analysis of the measured response, we obtain Q n After the (ω) term, H1(ω), H3(ω,ω,-ω) and H5(ω,ω,ω,-ω,-ω) can be determined by the least squares method. Near the resonance peak, a set of frequencies ω1 to ω are fitted by the estimated first-order FRF curve. Nf The linear stiffness and damping parameters are obtained, and the linear parameter solution equation is expressed as follows:

[0067]

[0068] The cubic stiffness term and cubic damping term parameter solution equations are expressed as follows:

[0069]

[0070] This allows the linear and nonlinear parameters in the nonlinear frequency response model of the robot end to be identified. Figure 5 As shown in the figure, the Runge-Kutta method is used to simulate the robot milling system using the identified dynamic parameters m, c1, k1, c3 and k3. The results show that the established nonlinear frequency response model including nonlinear damping c3 and nonlinear stiffness k3 can well capture the change of natural frequency and amplitude reduction of the robot milling system under different amplitude force excitations. The identified nonlinear frequency response of the robot end can accurately describe the dynamic response of the robot milling system under different excitation amplitudes.

[0071] S3, based on the obtained dynamic parameters, identifies the parameters of the spindle and tool holder joint, and combines the RCSA theory to predict the force / displacement frequency response function of the tool tip of the robotic milling system to achieve the modeling of the nonlinear frequency response of the tool tip of the robotic milling system.

[0072] Based on the nonlinear frequency response of the end of the robot-spindle-tool holder subsystem, the Timoshenko beam theory is used to model the dynamic characteristics of the tool substructure. Then, combined with the RCSA theory, the force / displacement frequency response function of the tool tip of the robot milling system is predicted, the parameters of the spindle and tool holder joint are identified, and the accurate modeling of the nonlinear frequency response of the tool tip of the robot-spindle-tool holder-tool system is achieved. Figure 6 The figure shows the substructure division diagram of the tool tip frequency response prediction of the robot milling system. The robot milling system is divided into the robot-spindle-tool holder substructure and the tool substructure, as well as the joint between the tool holder and the tool.

[0073] The dynamic characteristics of the tool substructure are modeled using Timoshenko beam theory, which offers higher modeling accuracy when dealing with short to medium-length beams and structures with high-frequency vibrations. In this implementation, the use of Timoshenko beam theory to model the tool substructure more accurately describes its dynamic response during machining. By combining the finite difference method with the RCSA substructure coupling approach and using experimental data, a particle swarm optimization algorithm is employed to optimize and identify the stiffness and damping parameters of the shank-tool interface, thereby achieving highly accurate prediction of the nonlinear frequency response characteristics of the tool tip.

[0074] According to the RCSA theory, the frequency response calculation equation of the robot-spindle-tool holder-tool assembly end can be obtained, where the matrix G 11 The element (1,1) is the required force / displacement frequency response function of the tool tip of the robot milling system:

[0075] G 11 =R 11 -R 13a B -1 R 3a1

[0076] Where B = R 3a3a +R 3b3b +R J , where R J The response matrix of the joint between the robot-spindle-tool holder substructure and the tool substructure can be expressed as:

[0077]

[0078] Force / displacement frequency response function of the tool tip of the robot-spindle-tool system sht 11 There are four unknown joint parameters: k x 、k θ 、c x and c θ, these parameters are identified through experiments. In the main effective frequency range of the intercept, the force / displacement frequency response function e_g at the tool tip is measured experimentally. 11 And the frequency response function of the tool tip of the robot-spindle-tool holder-tool system, the following optimization objective function can be constructed to minimize the experimental data e_g 11 The modeling calculated value g 11 The error between:

[0079]

[0080] Where p={k x ,k θ ,r x ,r θ} is the parameter of the joint to be identified, g 11 is the calculated force / displacement frequency response function at the tool tip of the robot-spindle-tool holder-tool system, real and img represent the real and imaginary parts, respectively, and ω is the corresponding frequency, which is solved by the particle swarm optimization algorithm.

[0081] After identifying the joint parameters, the nonlinear frequency response prediction of the tool tip of the robot-spindle-tool holder-tool system can be further realized through the RCSA substructure coupling method on the basis of the nonlinear dynamics modeling of the robot milling system. The frequency response function of the tool tip of the robot milling system can be predicted based on different input force amplitudes. Figure 5 The nonlinear frequency response of the tool tip can be predicted by performing RCSA calculation on the end frequency response of the robot-spindle-tool handle subsystem and the tool substructure. Figure 7 (a) shows the nonlinear frequency response function of the tool tip point of the robot-spindle-tool holder-tool system obtained from the experimental test. Figure 7 Figure (b) shows the predicted nonlinear frequency response function. It can be observed that under different force amplitudes, the frequency response function of the tool end exhibits significant nonlinear characteristics, as evidenced by the shift in the natural frequency and the change in the response amplitude. As the excitation force amplitude increases, the natural frequency decreases to a certain extent, while the response amplitude also exhibits a nonlinear growth or attenuation trend. The proposed method can accurately describe the nonlinear dynamic characteristics of the tool end of the robotic milling system and successfully capture the dynamic changes of the system under different excitation conditions.

[0082] The equipment involved in this embodiment includes: a six-axis industrial robot, an electric spindle and a matching tool holder and tool, an electric dynamic exciter and a piezoelectric impedance head, a hammer test device, a laser vibrometer and an acceleration sensor.

[0083] The present invention also provides an application of the above-mentioned nonlinear frequency response modeling method of the terminal end of the robotic milling system in the vibration characteristics and stability prediction of the robotic milling system and the processing control of the robotic milling system.

[0084] The present invention also provides a nonlinear frequency response modeling system for the terminal end of a robotic milling system. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the nonlinear frequency response modeling method for the terminal end of the robotic milling system as described above.

[0085] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the above-mentioned method for modeling the nonlinear frequency response of the end of the robotic milling system.

[0086] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A nonlinear frequency response modeling method for the end of a robot milling system, characterized in that: The method comprises the following steps: S1, establish the nonlinear frequency response model of the robot terminal through experimental analysis; S2, identifying the linear dynamic parameters and nonlinear dynamic parameters of the nonlinear frequency response model by a harmonic detection method, and analyzing the nonlinear response of the robot milling system based on Volterra series; S3, based on the obtained dynamic parameters, identifies the parameters of the spindle and tool holder joint, and combines the RCSA theory to predict the force / displacement frequency response function of the tool tip of the robotic milling system to achieve the modeling of the nonlinear frequency response of the tool tip of the robotic milling system.

2. The nonlinear frequency response modeling method for a robot milling system terminal according to claim 1, wherein: The mathematical expression of the nonlinear frequency response model is: Where F(t) is the manipulator end-operation force vector; M, C, and K are the mass, stiffness, and damping matrices of the robot system, respectively; q(t) is the displacement of the robot end in Cartesian space; C3 and K3 correspond to the cubic nonlinear damping matrix and the cubic nonlinear stiffness matrix, respectively.

3. The method for modeling the nonlinear frequency response of a robot milling system terminal according to claim 2, wherein: The identification of dynamic parameters in the nonlinear frequency response of the robot end is achieved through an identification method based on the restoring force surface method.

4. The method for modeling the nonlinear frequency response of a robot milling system terminal according to claim 1, wherein: The nonlinear stiffness and damping parameters of the nonlinear frequency response model are identified by a harmonic detection method.

5. The method for modeling the nonlinear frequency response of a robot milling system terminal according to claim 2, wherein: The solution equation for the linear dynamic parameters is: The equations for solving the parameters of the cubic stiffness term and the cubic damping term are: The linear stiffness coefficient and damping coefficient are: The cubic stiffness coefficient and cubic damping coefficient are: H3(ω,ω,-ω)=(-ic3ω 3 -k3)H1(ω) 3 H1(-ω) Where m, c1, and k1 are the linear mass, damping, and stiffness parameters, respectively; c3 and k3 are the cubic nonlinear damping and cubic nonlinear stiffness parameters, respectively; and ω represents the frequency.

6. The method for modeling the nonlinear frequency response of a robot milling system terminal according to claim 1, wherein: The robotic milling system is divided into a robot-spindle-toolholder substructure and a tool substructure. Based on the nonlinear frequency response of the end of the robot-spindle-toolholder subsystem, the Timoshenko beam theory is used to model the dynamic characteristics of the tool substructure, and then the RCSA theory is combined to predict the force / displacement frequency response function of the tool tip point of the robotic milling system.

7. The method for modeling the nonlinear frequency response of a robot milling system terminal according to claim 6, wherein: The force / displacement frequency response function of the tool tip of the robot milling system is: G 11 =R 11 -R 13a B -1 R 3a1 Where B = R 3a3a +R 3b3b +R J , where R J represents the joint response matrix between the robot-spindle-tool holder substructure and the tool substructure, and the corresponding expression is: Where k x and c x represents the linear spring stiffness and linear damping parameters, k θ and c θ are the torsional spring stiffness and torsional damping parameters, respectively, and are the parameters of the joint between the tool handle and the tool.

8. An application of the nonlinear frequency response modeling method of a robot milling system terminal according to any one of claims 1 to 7 in the vibration characteristics and stability prediction of the robot milling system and the machining control of the robot milling system.

9. A nonlinear frequency response modeling system for a robot milling system terminal, characterized by: The system includes a memory and a processor, the memory stores a computer program, and the processor executes the nonlinear frequency response modeling method of the robot milling system terminal according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the nonlinear frequency response modeling method of the end terminal of the robot milling system according to any one of claims 1 to 7.

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